We establish two bounds on the gradient components. To do so, the bounds in Assumption REF  are used, with an appropriate restriction on \(\xi _{\rm {low}}\) . We then show that the first gradient component converges to 0 under certain conditions.
Let us start with the following lemma, which is an extension of [1]}: this holds for \(\xi _{\rm {low}}= \xi ^{\rm {up}}= 1\)  and it is stated for the components of the error, that enjoy the same recursive formula as the components of the gradient.
